Question

statements reasons

1. ( p parallel q ) 1.
2. ( angle 1 cong angle 2 ) 2.
3. ( angle 2 cong angle 3 ) 3.
4. ( angle 3 cong angle 4 ) 4.
5. ( angle 1 cong angle 4 ) 5.

Explanation:

Step1: Identify \(p\parallel q\)

Given.

Step2: Prove \(\angle1\cong\angle2\)

Vertical angles are congruent.

Step3: Prove \(\angle2\cong\angle3\)

Alternate - interior angles (since \(p\parallel q\) and the transversal).

Step4: Prove \(\angle3\cong\angle4\)

Vertical angles are congruent.

Step5: Prove \(\angle1\cong\angle4\)

Transitive property of congruence (\(\angle1\cong\angle2\), \(\angle2\cong\angle3\), \(\angle3\cong\angle4\) implies \(\angle1\cong\angle4\)).

Answer:

1. Given; 2. Vertical angles are congruent; 3. Alternate - interior angles (for parallel lines \(p\) and \(q\) and the transversal); 4. Vertical angles are congruent; 5. Transitive property of congruence.